IMPROVED FINITE-DIFFERENCE METHOD FOR EQUILIBRIUM PROBLEMS BASED ON DIFFERENTIATION OF THE PARTIAL-DIFFERENTIAL EQUATIONS AND THE BOUNDARY-CONDITIONS

A numerical algorithm for producing high-order solutions for equilibri um problems is presented. The approximated solutions are improved by d ifferentiating both the governing partial differential equations and t heir boundary conditions. The advantages of the proposed method over s tandard finite difference methods are: the possibility of using arbitr ary meshes; the possibility of using simultaneously approximations wit h different (distinct) orders of accuracy at different locations in th e problem domain; an improvement in approximating the boundary conditi ons; the elimination of the need for 'fictitious' or 'external' nodal points in treating the boundary conditions. Furthermore, the proposed method is capable of reaching approximate solutions which are more acc urate than other finite difference methods, when the same number of no dal points participate in the local scheme. A computer program was wri tten for solving two-dimensional problems in elasticity. The solutions of a few examples clearly illustrate these advantages.